Question: Solve for $x$ : $x^2 - 3x - 40 = 0$
Solution: The coefficient on the $x$ term is $-3$ and the constant term is $-40$ , so we need to find two numbers that add up to $-3$ and multiply to $-40$ The two numbers $-8$ and $5$ satisfy both conditions: $ {-8} + {5} = {-3} $ $ {-8} \times {5} = {-40} $ $(x {-8}) (x + {5}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -8) (x + 5) = 0$ $x - 8 = 0$ or $x + 5 = 0$ Thus, $x = 8$ and $x = -5$ are the solutions.